Problem: Solve for $x$ and $y$ using elimination. ${-2x-2y = -20}$ ${2x-5y = 6}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $-7y = -14$ $\dfrac{-7y}{{-7}} = \dfrac{-14}{{-7}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {-2x-2y = -20}\thinspace$ to find $x$ ${-2x - 2}{(2)}{= -20}$ $-2x-4 = -20$ $-2x-4{+4} = -20{+4}$ $-2x = -16$ $\dfrac{-2x}{{-2}} = \dfrac{-16}{{-2}}$ ${x = 8}$ You can also plug ${y = 2}$ into $\thinspace {2x-5y = 6}\thinspace$ and get the same answer for $x$ : ${2x - 5}{(2)}{= 6}$ ${x = 8}$